100-Gbit/s Integrated Quantum Random Number Generator Based on Vacuum Fluctuations

Emerging communication and cryptography applications call for reliable fast unpredictable random number generators. Quantum random number generation allows for the creation of truly unpredictable numbers due to the inherent randomness available in quantum mechanics. A popular approach is to use the quantum vacuum state to generate random numbers. While convenient, this approach has been generally limited in speed compared to other schemes. Here, through custom codesign of optoelectronic integrated circuits and side-information reduction by digital filtering, we experimentally demonstrate an ultrafast generation rate of 100 Gbit/s, setting a new record for vacuum-based quantum random number generation by one order of magnitude. Furthermore, our experimental demonstrations are well supported by an upgraded device-dependent framework that is secure against both classical and quantum side information and that also properly considers the nonlinearity in the digitization process. This ultrafast secure random number generator in the chip-scale platform holds promise for next-generation communication and cryptography applications.

Popular Summary

Truly random numbers are a key component for many applications ranging from fundamental science to engineering. Quantum-mechanical phenomena have proven to be particularly strong sources of entropy thanks to their intrinsic randomness. In this work we exploit the randomness present in the vacuum state as a source of entropy to implement a high-speed integrated quantum random-number generator. To produce random numbers, we first amplify the vacuum noise using a chip-level homodyne detector. Next, we quantize the measurements and distill random numbers from the quantized data. To quantify how many random bits can be distilled from each measured sample, we employ a security framework that maps the amount of side information. We identify two separate sources of side information: a classical one, caused by additional electrical noise on top of the vacuum noise, and a quantum one, which arises from the environment being entangled with the system used to extract the random numbers. It is important to minimize the information leakage through these side-information channels to achieve a high-performance generator. We limit the amount of classical side information by using custom integrated devices optimized for low-noise operation. To minimize the amount of quantum side information we apply digital equalization, drastically reducing the correlation between subsequent samples. These efforts result in a high generation rate of 100 Gbps, which is an order of magnitude faster compared to the current state of art. We believe that this random-number generator is a key enabler for high-speed cryptography and quantum key distribution systems.

Figure 1

The block diagram for a quantum random number generator based on the quadrature measurement of the vacuum state $|0⟩$.

Figure 2

(a) The step response of a fictitious 3-bit ADC with nonlinear behavior. The solid blue trace represents the actual response of the ADC and the dashed gray line represents the ideal step response. The solid red line is the analog input applied to the ADC. (b) The differential nonlinearity (DNL) of the ADC. (c) The integral nonlinearity (INL) of the ADC. (d) The output distribution of the 3-bit ADC assuming that an input with a Gaussian density function is applied. The solid blue bars represent the actual response of the ADC, the dashed black line represents the response of an ideal 3-bit ADC, and the solid red line represents the analog input.

Figure 3

(a) The min-entropy for 4-, 8-, 12-, and 16-bit ADC resolution versus the temporal correlation factor ${\sigma }_M^2/{\sigma }_{M,c}^2$. Here, ${\sigma }_{M,c}^2$ and ${\sigma }_M^2$ are the conditional and unconditional variance of the homodyne measurement, respectively. The shaded areas indicate the regions for the ADC linearity varying between a bin width $\mathrm{\Delta }x=1$ LSB (the upper trace) and a bin width $\mathrm{\Delta }x=2$ LSB (the lower trace). (b) The min-entropy for 4-, 8-, 12-, and 16-bit ADC resolution versus the dc clearance level. The solid traces represent the scenario where the clearance is constant over the complete frequency range. The dashed traces represent the scenario where the clearance follows a second-order Butterworth response with a bandwidth of $\frac{f_N}{5}$. The assumption is made here that the ADC is ideal and that the temporal correlations are equal to one.

Figure 4

The block diagram for a zero-forcing linear equalizer [29]. $|0⟩$ represents the input shot noise, $Q_k$ represents the shot noise sampled after passing through the detector at time $k$, $E_k$ represents the excess noise, and $M_k$ represents the outcome of the homodyne measurement.

Figure 5

An overview of the QRNG setup. (a) The vacuum noise that is used as a source to generate random numbers. (b) A micrograph of the manufactured PIC and TIA. (c) The Gaussian distribution after digitization. (d) The distribution of the distilled random 32-bit integers, grouped into 256 bins.

Figure 6

(a) A heat map of the errors present in the captured sine wave. The inset shows the distributions for the codes $-50$, 0, and 100. The blue line represents the INL, i.e., the mean of the errors for each digitization result. (b) The integral nonlinearity versus the ADC code. (c) The differential nonlinearity versus the ADC code.

Figure 7

The homodyne-measurement PSD $S_M(f)$, excess-noise PSD $S_E(f)$, and clearance $C(f)$ for the cases where: (a) no equalizer, (b) an equalizer up to 8 GHz, and (c) an equalizer up to 10 GHz are used.

Figure 8

The effect of the equalizers on the autocorrelation. The autocorrelation coefficients are averaged over 10 000 measured data sets.